2 Part A). This part is basically asking you to look at the diagram and read the length of one wave. Part B). Here, you need to use the equation above (for the fundamental frequencies of the standing waves on a string) and solve it for . When you do that, look carefully at which n value will give the largest wavelength, then solve using the given numbers. Part C). Here, you can use either the equation or to determine the wave speed on the string. Note that when you see “fundamental” frequency, the antinode number ( n ) is 1. Part D). Check the diagrams above, or make your own! Notice that the overtones start after the fundamental, and the first overtone (or harmonic) has two antinodes, not one. Thus, count accordingly. Part E). The lowest frequency must be the fundamental, and remember that octaves are exact multiples in the ratio of 2:1. Thus, you can easily figure out the situation with the higher frequencies listed for this part. Problem 2 “Two Identical Pulses along a String” Part A). This is very basic, as long as you remember that when waves reflect off fixed boundaries, they invert, returning 180° out of phase. When waves reflect off a weak (or loose) boundary, they reflect non-inverted, or go back with the amplitude pointing in the same direction (in phase with the original pulse).

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